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Jobisdone [24]
3 years ago
13

Assume that the total revenue received from the sale of x items is given​ by, ​R(x)equals34 ln (4 x plus 5 )​, while the total c

ost to produce x items is ​C(x)equalsx divided by 2. Find the approximate number of items that should be manufactured so that​ profit, ​R(x)minus​C(x), is a maximum.
Mathematics
1 answer:
katen-ka-za [31]3 years ago
5 0

Answer:

63 units

Step-by-step explanation:

The profit function P(x) is given by the revenue function minus the cost function:

P(x) = R(x) - C(x)\\P(x) = 34ln(x+5)-\frac{x}{2}

The number of units sold 'x' for which the derivate of the profit function is zero, is the number of units that maximizes profit:

P(x) = 34ln(x+5)-\frac{x}{2}\\P'(x) =0= \frac{34}{x+5}-\frac{1}{2}\\x+5=68\\x=63\ units

The number of units that should be manufactured so that​ profit is maximum is 63 units.

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